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amanvermagmat
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In a recently held cricket tournament in one of the universities 23 Feb 2018, 23:48
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A
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95% (hard)

Question Stats:

36% (02:40) correct 64% (02:27) wrong based on 210 sessions

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In a recently held cricket tournament in one of the universities in Australia, 'N' teams participated in total. The tournament comprised of various rounds, where each round comprised of one or more 'games'. Each 'game' was always between two teams only, and the rules were designed as such that each 'game' resulted in a Win for one team and Loss for the other team, there were no Draws.
What is the value of 'N'?

(1) In the first round of the tournament, each team played a game with every other team, and no two teams played each other more than once. This way, '28' games in total were played in round 1.

(2) Out of 'N', 4 teams were selected after round 1 for round 2, where '2' games were played in total; and 2 teams were selected from round 2 for round 3, where there was only '1' game played that declared the winner. Thus, tournament was over in 3 rounds. This way, in total, '31' games were played in the entire tournament.
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In a recently held cricket tournament in one of the universities 24 Feb 2018, 02:26
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amanvermagmat
In a recently held cricket tournament in one of the universities in Australia, 'N' teams participated in total. The tournament comprised of various rounds, where each round comprised of one or more 'games'. Each 'game' was always between two teams only, and the rules were designed as such that each 'game' resulted in a Win for one team and Loss for the other team, there were no Draws.
What is the value of 'N'?

(1) In the first round of the tournament, each team played a game with every other team, and no two teams played each other more than once. This way, '28' games in total were played in round 1.

(2) Out of 'N', 4 teams were selected after round 1 for round 2, where '2' games were played in total; and 2 teams were selected from round 2 for round 3, where there was only '1' game played that declared the winner. Thus, tournament was over in 3 rounds. This way, in total, '31' games were played in the entire tournament.
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We're asked to find the number of teams.
Let's see which statements give us relevant information, a Logical approach.

(1) This gives us an equation with one variable: N choose 2 = 28 and is therefore solvable.
Sufficient!

(2) so we know that the first round had 31 - 1 - 2 = 28 games but we don't know how they were distributed amongst the teams.
Therefore we cannot create an equation connecting the number of teams to the number of games in round 1.
Insufficient.

(A) is our answer.
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In a recently held cricket tournament in one of the universities 08 Mar 2018, 01:20
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Hi, I have a question.

For statement 1: Do we assume that all teams in the tournament participated in Round 1 of the tournament or some teams will skip round 1 as they are directly qualify for the 2nd round. As round 1 could be just qualifier rounds for selected under-dog teams, out of which X teams will be selected and join the other directly qualified teams in Round 2.

Can someone please help? I feel little bit confused. Sorry i may sound silly. But just to get clarified, in case CAT throws me such questions on my D-Day

Thanks.
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In a recently held cricket tournament in one of the universities 08 Mar 2018, 01:59
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hellosanthosh2k2
Hi, I have a question.

For statement 1: Do we assume that all teams in the tournament participated in Round 1 of the tournament or some teams will skip round 1 as they are directly qualify for the 2nd round. As round 1 could be just qualifier rounds for selected under-dog teams, out of which X teams will be selected and join the other directly qualified teams in Round 2.

Can someone please help? I feel little bit confused. Sorry i may sound silly. But just to get clarified, in case CAT throws me such questions on my D-Day

Thanks.
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Hello Santhosh

In statement 1 it is mentioned: "each team played a game with every other team, and no two teams played each other more than once. This way, '28' games in total were played in round 1". I think this should clarify your query. All teams participated and each team played with every other team, just once.
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In a recently held cricket tournament in one of the universities 09 Apr 2019, 20:29
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DavidTutorexamPAL
amanvermagmat
In a recently held cricket tournament in one of the universities in Australia, 'N' teams participated in total. The tournament comprised of various rounds, where each round comprised of one or more 'games'. Each 'game' was always between two teams only, and the rules were designed as such that each 'game' resulted in a Win for one team and Loss for the other team, there were no Draws.
What is the value of 'N'?

(1) In the first round of the tournament, each team played a game with every other team, and no two teams played each other more than once. This way, '28' games in total were played in round 1.

(2) Out of 'N', 4 teams were selected after round 1 for round 2, where '2' games were played in total; and 2 teams were selected from round 2 for round 3, where there was only '1' game played that declared the winner. Thus, tournament was over in 3 rounds. This way, in total, '31' games were played in the entire tournament.

We're asked to find the number of teams.
Let's see which statements give us relevant information, a Logical approach.

(1) This gives us an equation with one variable: N choose 2 = 28 and is therefore solvable.
Sufficient!

(2) so we know that the first round had 31 - 1 - 2 = 28 games but we don't know how they were distributed amongst the teams.
Therefore we cannot create an equation connecting the number of teams to the number of games in round 1.
Insufficient.

(A) is our answer.
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In statement 2 we get to know that in round 1 there were 28 games, isn't that the same as data provided in statement 1 ?
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In a recently held cricket tournament in one of the universities 28 Apr 2019, 16:19
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anmolsd1995


In statement 2 we get to know that in round 1 there were 28 games, isn't that the same as data provided in statement 1 ?
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Hey anmolsd1995,

First, apologies for the delayed response. (In general, please PM me if you wish to make sure I see your reply).

In the given data we are not told the structure of the tournament (all we know is that each 'game' was played between two teams). So while we know from stmt 2 that round 1 contained 28 games, we do not know how many teams played these games. Was it best of 5? One match per every pair of teams? 7 teams with only the top 4 passing onwards? Without information on the structure, we cannot know and therefore (2) is insufficient.
Note that the information provided in (1) hints that this is the solution -- (1) is sufficient precisely because it provides information on the structure of the tournament and so you should, when looking at (2), wonder if it gives the same (or equivalent) information.

Best,
David
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In a recently held cricket tournament in one of the universities 07 Jun 2026, 11:51
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For statement 1 we know that there 28 games and its round robin i.e. situation i.e. Each team plays every team once hence

n (n-1) = 56/2. N can only be 8 Sufficient

But in statement 2 we know that there were 28 games ---> but do we know whether it was round robin or not ? NOPE
Do we know how the games were distributed to find the number of teams ? NOPE

For all we know there could be 8 teams ---> with round robin
or 5 ,6, 7 or any number of teams with some teams playing a few matches and others playing more or some playing none ---> and ultimately 4 teams advancing based on some calculation.

Key point here is not to bring in any real world biases --> you may think there is no practical way of distributing 28 games among teams other than 8 or you may end up wasting time by trying to find any combination of teams other than 8 to fit in with 28 games ---> that ll be a waste of time in such DS questions.

Hence A
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